Moses was born in New York City, New York, on February 24, 1958, but grew up in Evanston, Illinois. His father worked in advertising on Madison Avenue while they lived in New York City; Moses later claimed that this helped him when he landed the role of Duck Phillips on Mad Men. Moses's parents later moved to Saint Louis, Missouri, while he was still in high school, so he stayed with family friends in Evanston to finish his high-school education at Evanston Township High School, where he was the quarterback of the school's varsity football team. He then enrolled at Ithaca College in Ithaca, New York, where he majored in English. Moses later dropped out after a year to travel. He then enrolled at New York University, where he graduated with a degree in theater. He then started an acting career in 1985.

Moses has since appeared in a number of films directed by Oliver Stone, including Platoon, The Doors, and Born on the Fourth of July. He also starred in a variety of projects, including Big Momma's House 2 and Star Trek: Voyager. However, he did not gain fame until he was cast as Paul Young on the hit ABC drama-comedy series Desperate Housewives. He later portrayed Herman "Duck" Phillips on the AMC-produced series Mad Men until 2009; this was another well-known role of his. Moses also appeared off-Broadway, playing the titular character, "a Wall Street creep", in a 2006 play called Burleigh Grimes.